Are there opportunities for some us non-geniuses to get a scholarship to Harvard?
Sure. You don’t have to be a genius at all to attend Harvard. From what I know, you only need good CGPAs, good GRE and TOEFL/IELTS scores, and good letters of recommendation, which…well, many people have.
One way to have a full scholarship is to get it through another awarding body. But Harvard is a generous school. They give lots of full scholarships to underprivileged students who make into their programs.